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3 years ago

Consider the functions:

Mathematics

1 answer:

inn [45]3 years ago

6 0

Answer:

The function f(x) was translated right 3 units and up 2 units

Step-by-step explanation:

<em>k </em>= 2, which is denoted as vertical movement

<em>b </em>= -3, which is denoted to horizontal movement

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Desmond deposits $50 into a savings account every month at an annual interest rate of

joja [24]

Given:

Desmond deposits $ 50 monthly.

Yearly he deposits = $50×12 = $ 600

Rate of interest compounded monthly = 4.7%

To find the amount he will receive after 10 years and the rate of change the value of his account after 10 years.

Formula

$A = P(1+\frac{r}{(n)(100)} )^{nt}$

where,

A be the final amount

P be the principal

r be the rate of interest

t be the time and

n be the number of times the interest is compounded.

Now,

Taking,

P = 600, r = 4.7, n = 12, t = 10 we get,

$A = 600(1+\frac{4.7}{(12)(100)}) ^{(12)(10)}$

or, $A = 600(1.0039)^{120}$

or, $A = 959.1$

Now,

At starting he has $ 600

At the end of 10 years he will be having $ 959.1

So,

The amount of change in his account = $ (959.1-600) = $ 359.1

Therefore the rate of change = $(\frac{359.1}{600} )(100) %$

= 59.85%

Hence,

a) His account will contain $ 959.1 after 10 years.

b) The rate of change in his account is 59.85% after 10 years.

7 0

3 years ago

in class of 40 students report that english is their favorite class 40 percent of the students report that keyboard is there fav

olasank [31]

If 40% of students prefer keyboarding, 40/100*40=16 students like it best. If the remaining students prefer English, then 40-16=24 students like English best. Since 24 is more than 16, most students prefer English.

4 0

3 years ago

HELP WITH 20 PLEASE!

WINSTONCH [101]

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Question from Amanda, a parent:

what is the area of a circle with a circumference of 3000 metres?

Amanda,

The area of a circle is given by the formula A = π r2, where A is the area and r is the radius. The circumference of a circle is C = 2 π r.

If we "solve for r" in the second equation, we have r = C / (2 π ). Now we use this to replace r in the first equation: A = π [ C / (2 π ) ]2.

When we simplify this, we get A = C2 / (4 π).

Now you can put your value of C into this equation and find A. Remember, π is about 3.1416.

6 0

3 years ago

kicyunya [14]

Answer:

8.69% probability that at least 285 rooms will be occupied.

Step-by-step explanation:

For each booked hotel room, there are only two possible outcomes. Either there is a cancelation, or there is not. So we use concepts of the binomial probability distribution to solve this question.

However, we are working with a big sample. So i am going to aproximate this binomial distribution to the normal.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

In this problem, we have that:

A popular resort hotel has 300 rooms and is usually fully booked. This means that $n = 300$

About 7% of the time a reservation is canceled before the 6:00 p.m. deadline with no pen-alty. What is the probability that at least 285 rooms will be occupied?

Here a success is a reservation not being canceled. There is a 7% probability that a reservation is canceled, and a 100 - 7 = 93% probability that a reservation is not canceled, that is, a room is occupied. So we use $p = 0.93$